Simplify the following expression: $ x = \dfrac{-1}{6} + \dfrac{-2}{r - 9} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r - 9}{r - 9}$ $ \dfrac{-1}{6} \times \dfrac{r - 9}{r - 9} = \dfrac{-r + 9}{6r - 54} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-2}{r - 9} \times \dfrac{6}{6} = \dfrac{-12}{6r - 54} $ Therefore $ x = \dfrac{-r + 9}{6r - 54} + \dfrac{-12}{6r - 54} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-r + 9 - 12}{6r - 54} $ $x = \dfrac{-r - 3}{6r - 54}$